Experimental Probes and Facilities

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ARPES

ARPES (Angle-Resolved Photoemission Spectroscopy) is an experimental technique based on several refinements of the photoelectric effect initially observed by Heinrich Hertz in 1887.
When photons of a well-defined energy hν are incident upon a sample, measurement of the electron's kinetic energy and exit angle gives information about the momentum and energy of
the electron state in the material. In particular, ARPES data directly gives the binding energy of the emitted electrons and the components of momentum parallel to the surface.
However, since the electrons interact with the surface upon emission, less information is given relating to momentum in the direction normal to the sample surface.
More explicitly, if a photoemitted electron leaves the sample with kinetic energy Ekin at an angle θ to the normal, its binding energy
and momentum parallel to the surface are given by Ebind = hν - φ - Ekin and p// = (2 m Ekin)1/2 sinθ, where φ is the material's work function.
The physical quantity directly related to the measured photoemission intensity is the "one-particle spectral function" A(k,ω) = Σ''(k,ω) / (π [ω - εk - Σ'(k,ω)]2 + πΣ''(k,ω)2)
where the functions Σ are the components of the electron self-energy, which describes the interactions between the electron and the other particles in the system and is of
great theoretical interest, as they describe the energy and lifetime of elementary excitations in the material.

To obtain high-quality data, ARPES experiments are conducted in an ultra-high vacuum chamber which minimizes surface contamination and interactions between the photoemitted electrons and any potential
interference between the emission and detection processes. Additionally, ARPES experiments are often performed at cryogenic temperatures to minimize thermal broadening of the data. This capability also
allows for the study of high-temperature superconductors below their critical temperatures, where the electrons take on a fundamentally different structure.

The technique has opened many doors in the study of crystalline solids such as high-temperature superconductors, graphene, and topological insulators each of which is particularly suited to ARPES
due to their two-dimensional nature. In particular, ARPES has been used to map out Fermi surfaces in these materials, like those for the cuprate (left) and iron pnictides (right) shown above. ARPES has also
been used to explore the superconducting gap and pseudogap of cuprate superconductors as a function of temperature and momentum.

Synchrotron ARPES

Synchrotron ARPES offers flexibility in terms of being able to easily vary photon energy, which makes it easy to optimize matrix element effects (which describe the interaction between the electromagnetic
field and the electrons in the sample) to the parameters of different samples which otherwise limit the usefulness of ARPES spectra. With high photon energies (15-150 eV), electrons from a large area of momentum
space are photoemitted and thus available for study. For many samples, electrons from the first several Brillouin zones can be photoemitted and thus mapped out using synchrotron ARPES. Our group uses synchrotron radiation from the
Advanced Light Source (ALS) at Lawrence Berkeley National Lab, utilizing several different beamlines: HERS at BL 10.0.1, Angle and Spin-resolved Photoemission at BL 12.0.1, and MERLIN at BL 4.0.3.

Laser ARPES

In order for a photoemission experiment to work, the photon energy hν must be greater than the work function φ of the material being probed. Developments in nonlinear optics have
led to systems of nonlinear crystals which can take 1.5 eV photons from a titanium sapphire laser and create a fourth harmonic at 5.9 eV. This photon energy is sufficient to induce
photoemission in many samples, and is used in our lab. This lower energy results in a higher momentum resolution for a given angular resolution when compared to experiments performed with
synchrotron radiation. As a tradeoff, less of momentum space is available for study.